Global gradient estimates for the p(⋅)-Laplacian

2013/12/19 by Diening, Lars, Schwarzacher, Sebastian
#35J60 35B65 35B45 35Q35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1312.5570

Abstract

We consider Calderón-Zygmund type estimates for the non-homogeneous p(⋅)-Laplacian system -div(|D u|^p(⋅)-2 Du) = -div(|G|^p(⋅)-2 G), where p is a variable exponent. We show that |G|^p(⋅) ∈ L^q(ℝⁿ) implies |D u|^p(⋅) ∈ L^q(ℝⁿ) for any q ≥ 1. We also prove local estimates independent of the size of the domain and introduce new techniques to variable analysis.

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